The stability and stabilization of Markov jump linear systems with regime cluster

This paper is concerned with the stability and stabilization analysis for another usual class of Markov jump linear systems(MJLSs). In this paper, some of the system's regimes are difficult or unable to classify accurately, and this problem can be solved via recombined the probability space of the system. As a result, the necessary and sufficient conditions for stochastic stability of the system are showed below. Finally, numerical example is provided to show the validity of the method. There are also some expectation about the application of the method used in this paper in the end.